Musculoskeletal models of the shoulder complex are valuable research aids to investigate tears of the supraspinatus and the resulting mechanical impact during abduction of the humerus. One of the major contributors to this motion is the deltoid muscle group and for this, an accurate modeling of the lines of action is indispensable. The aim of this work was to utilize a torus obstacle wrapping approach for the deltoids of an existing shoulder model and assess the feasibility of the approach during humeral abduction. The shoulder model from the AnyBody™ modeling system was used as a platform. The size of the tori is based on a magnetic resonance imaging (MRI) approach and several kinematic couplings are implemented to determine the trajectories of the tori during abduction. To assess the model behavior, the moment arms of the virtual muscle elements and the resultant glenohumeral joint reaction force (GHJF) were compared with reference data from the literature during abduction of the humerus in the range 20°–120°. The root mean square error for the anterior, lateral and posterior part between the simulated muscle elements and reference data from the literature was 3.9, 1.7 and 5.8 mm, respectively. The largest deviation occurred on the outer elements of the muscle groups, with 12.6, 10.4 and 20.5 mm, respectively. During abduction, there is no overlapping of the muscle elements and these are in continuous contact with the torus obstacles, thus enabling a continuous force transmission. This results in a rising trend of the resultant GHJF.

The torus obstacle approach as a wrapping method for the deltoid muscles provides a guided muscle pathing by simultaneously approximating the curvature of the deltoid muscle. The results from the comparison of the simulated moment arms and the resultant GHJF are in accordance with those in the literature in the range 20°–120° of abduction.

Although this study shows the strength of the torus obstacle as a wrapping approach, the method of fitting the tori according to MRI data was not suitable. A cadaver study is recommended to better validate and mathematically describe the torus approach.

肩部复合体的肌肉骨骼模型是有价值的研究辅助工具，可用来研究肱骨上tear的撕裂以及在肱骨外展期间产生的机械冲击。三角肌群是促成这一运动的主要因素之一，为此，精确地模拟动作路线是必不可少的。这项工作的目的是针对现有肩部模型的三角肌采用环面障碍物包裹方法，并在肱骨外展期间评估该方法的可行性。来自AnyBody™建模系统的肩部模型被用作平台。花托的大小基于磁共振成像（MRI）方法，并且通过几种运动学耦合来确定绑架过程中花托的轨迹。为了评估模型行为，在骨骼外展时，在20°–120°范围内，将虚拟肌肉元件的力矩臂和产生的盂肱关节反作用力（GHJF）与文献中的参考数据进行了比较。模拟的肌肉元素与文献的参考数据之间的前，外侧和后部的均方根误差分别为3.9、1.7和5.8 mm。最大的偏差发生在肌肉群的外部元素上，分别为12.6、10.4和20.5 mm。在绑架过程中，肌肉元素没有重叠，并且这些肌肉元素与环面障碍物连续接触，从而实现了连续的力传递。这导致所得GHJF的上升趋势。

圆环障碍物方法作为三角肌的包裹方法，通过同时逼近三角肌的曲率来提供引导的肌肉路径。比较模拟力矩臂和所得GHJF的结果与文献中绑架20°–120°范围内的结果一致。

尽管这项研究显示出圆环障碍物作为包裹方法的强度，但根据MRI数据拟合圆环的方法并不适合。建议进行尸体研究，以更好地验证和数学描述圆环方法。